Toward fits to scaling-like data, but with inflection points & generalized Lavalette function

摘要: Experimental and empirical data are often analyzed on log-log plots in order to find some scaling argument for the observed/examined phenomenon at hands, particular rank-size rule research, but also critical phenomena thermodynamics, fractal geometry. The fit a straight line such is not always satisfactory. Deviations occur low, intermediate high regimes along log($x$)-axis. Several improvements of mere power law discussed, through Mandelbrot trick low rank Lavalette cut-off rank. In so doing, number free parameters increases. Their meaning up 5 parameter super-generalized 7-parameter hyper-generalized law. It emphasized that interest basic 2-parameter subsequent generalizations resides its "noid" (or sigmoid, depending sign exponents) form semi-log plot; something incapable be found other law, like Zipf-Pareto-Mandelbrot remained completeness invent simple showing an inflection point \underline{log-log plot}. Such can result from transformation $x$ $\rightarrow$ log($x$), this theoretically unclear. However, linear combination two shown provide requested feature. Generalizations taking into account or laws suggested, need fully considered time appropriate data.